Question

If the variance of the random variable $X$ is $4$, then the variance of the random variable $5X+10$ is

• A. $100$
• B. $10$
• C. $50$
• D. $25$

Answer 1

The correct option is A $100$

If a random variable X is adjusted by multiplying by the value b and adding the value a, then the variance is affected as follows: ${\sigma }_{a+bX}^2=b^2{\sigma }^2$
If the variance of the random variable X = ${\sigma }^2$ = 4
For the random variable $5X+10$,

${\sigma }_{10+5X}^2=b^2{\sigma }^2=5^{2}4=100$
${\sigma }_{10+5X}^2=100$